However, if EA were to suddenly shut down Origin and render copies of Crysis 2 or Dragon Age 2 useless without providing alternative means to play the games offline, then they would effectively be committing theft, not to mention violating their own EULA.
Really? Do they promise in their EULA to guarantee access to "one's" games in Origin? What exactly do they say, ie. guaranteed access from here to eternity, or x months or years from the day of purchase?
As far as I've read e.g. the Steam TOS/EULA, they make none such guarantees. Mostly they just state that the service is terminable, and that's that. If it means you can't play your Steam games, tough. (Naturally, as long as they are operational, they would probably mostly avoid that due to bad press (not legality)).
Also I don't quite understand why you make a distinction between multiplayer or single-player games. Frankly, I don't think laws make any kind of distinction between them, if both need some external servers and services to be operational. I'm pretty sure the only thing that binds the "service providers" is that you are guaranteed access for the time you have paid them, e.g. the next month.
Digital games where you pay only once in the beginning are in some kind of legal limbo. Maybe it depends on the court how long they feel you'd be entitled to play a game for which you've paid 50€. How about if you bought it on sale for 5€, is the playing time shorter in court's eyes?
The stuff Valve provides has generally been accepted by consumers as beneficial as a service. Consistent updates, occasional new content, achievements, cloud support, etc. If you want to see "games as a service" done in a consumer and media approved way look no further.
Most of this acceptance seems to be simply a misconception by many Steam users by what they are entitled to in order to access their games. Many haven't realized yet they have none whatsoever, which is partly understandable because the Steam pages talk about "purchasing games on Steam", as if it is the same as buying e.g. a retail console game or a DVD movie.
As long as people realized their (lack of) rights, and if they still are fine with that, fine.